MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties
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| Format: | Preprint |
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2026
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| _version_ | 1866913169950113792 |
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| author | Burger, Andreas Thiede, Luca Aldossary, Abdulrahman Campos-Gonzalez-Angulo, Jorge A. Zook, Alex Gonthier, Jérôme Florian Aspuru-Guzik, Alán |
| author_facet | Burger, Andreas Thiede, Luca Aldossary, Abdulrahman Campos-Gonzalez-Angulo, Jorge A. Zook, Alex Gonthier, Jérôme Florian Aspuru-Guzik, Alán |
| contents | Coupled-cluster (CC) theory is often considered the gold standard of quantum chemistry, but its high computational cost limits routine access to accurate energies, forces and response properties. While the right-hand $T$-amplitudes determine the correlated wavefunction, many practically important observables additionally require the left-hand $Λ$-amplitudes. We introduce MōLe-$Λ$, an extension of Molecular Orbital Learning (MōLe) that predicts the full ground-state coupled-cluster singles and doubles (CCSD) response state by jointly learning right-hand amplitudes $(T_1,T_2)$ and left-hand amplitudes $(Λ_1,Λ_2)$ from localized Hartree--Fock molecular orbitals. Architecturally, MōLe-$Λ$ extends MōLe with $Λ_1$ and $Λ_2$ readouts that mirror the symmetry constraints of the $T_1$ and $T_2$ heads, while preserving the original equivariant orbital encoder, odd sign-equivariant decoding, locality and size-extensivity. The resulting model yields accurate CC-quality energies and forces, while simultaneously recovering dipoles, quadrupoles, polarizabilities, the electron density, and 2-electron observables such as the pair density. We show that MōLe-$Λ$ further extends the speed advantage of MōLe over full CCSD while substantially expanding the accessible properties, providing a route to wavefunction-level surrogate models for correlated quantum chemistry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties Burger, Andreas Thiede, Luca Aldossary, Abdulrahman Campos-Gonzalez-Angulo, Jorge A. Zook, Alex Gonthier, Jérôme Florian Aspuru-Guzik, Alán Machine Learning Chemical Physics Coupled-cluster (CC) theory is often considered the gold standard of quantum chemistry, but its high computational cost limits routine access to accurate energies, forces and response properties. While the right-hand $T$-amplitudes determine the correlated wavefunction, many practically important observables additionally require the left-hand $Λ$-amplitudes. We introduce MōLe-$Λ$, an extension of Molecular Orbital Learning (MōLe) that predicts the full ground-state coupled-cluster singles and doubles (CCSD) response state by jointly learning right-hand amplitudes $(T_1,T_2)$ and left-hand amplitudes $(Λ_1,Λ_2)$ from localized Hartree--Fock molecular orbitals. Architecturally, MōLe-$Λ$ extends MōLe with $Λ_1$ and $Λ_2$ readouts that mirror the symmetry constraints of the $T_1$ and $T_2$ heads, while preserving the original equivariant orbital encoder, odd sign-equivariant decoding, locality and size-extensivity. The resulting model yields accurate CC-quality energies and forces, while simultaneously recovering dipoles, quadrupoles, polarizabilities, the electron density, and 2-electron observables such as the pair density. We show that MōLe-$Λ$ further extends the speed advantage of MōLe over full CCSD while substantially expanding the accessible properties, providing a route to wavefunction-level surrogate models for correlated quantum chemistry. |
| title | MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties |
| topic | Machine Learning Chemical Physics |
| url | https://arxiv.org/abs/2605.29622 |